[dcgriz]

I tried posting this yesterday but due to tablet errors I had to abort.....so here it goes again..

Although the role the spoke bracing angle has in determining the wheel lateral stiffness and stability/durability has been exhaustively discussed, I read post after post analyzing spoke quantity/type and rim weight without much consideration to hub geometry.

As a reminder, a higher bracing angle on the NDS offers higher wheel lateral stiffness. High lateral stiffness is desirable to conserve energy otherwise lost due to wheel flexing and also to the wheel rubbing onto the brake pads. I also happen to consider wheel rubbing to be an irritating nuisance, to be avoided when one builds a custom wheel. BUT, the higher the bracing angle the lesser the resulting tension on the NDS spokes becomes, down to the point where the lowered tension can not reliably prevent the spokes from loosening up when the wheel goes over a bump or simply due to repeated use, thus affecting the wheel's stability/durability. This becomes more prevalent when the rider is heavier (>200lbs), more powerfull (>500w) or imposes higher lateral forces (tilting the bike climbing standing up). A lighter rider capable of moderate output (300w) does not need to be concerned as much.

The following listings tabulate the calculated Bracing Angle Ratio (BAR) between the nds/ds spokes using Spokecalc. The tables also tabulate the resulting tension for the nds spokes (Tnds) using a formula accounting for the spoke length and flange offset ratios. This approach is envisioned as more accurate rather than simply taking the inverse of the BAR to calculate the tension ratio.

The rim used is a 23x28 with an ERD of 588. Lacing is with 32 spokes for the rear; results were similar for 28, I dont do 24 as is pointless, to me at least, to go after lateral stiffness if low spoke count is the primary consideration. In addition, I have not taken in consideration the adjustments in spoke stiffness and arrangement (heavier spokes on DS, triplet lacing, etc) that could be made to enhance stiffness. This just analyzes the effect of hub geometry, everything else kept equal.

Hubs cover a broad array from boutique to basic. Tension T values in kgf.

Alchemy ORC-UL-S10
ds/nds Tds Tnds BAR
3x/3x 125 67.4 1.9
2x/3x 125 69.8 1.8
3x/2x 125 65.8 1.9
2x/2x 125 68.2 1.8

Alchemy ORC-UL-S11/C11
ds/nds Tds Tnds BAR
3x/3x 125 58.9 2.1
2x/3x 125 61 2.1
3x/2x 125 57.6 2.2
2x/2x 125 59.6 2.1

CK R45 S11/C11
ds/nds Tds Tnds BAR
3x/3x 125 59.4 2.1
2x/3x 125 61.3 2.
3x/2x 125 57.6 2.2

WI T-11 S11/C11
ds/nds Tds Tnds BAR
3x/3x 125 53.4 2.3
2x/3x 125 55.3 2.3
3x/2x 125 52.2 2.4

BHS SL218
ds/nds Tds Tnds BAR
3x/3x 125 58.1 2.2
2x/3x 125 59.8 2.1
3x/2x 125 56.8 2.2

DT Swiss 240*
ds/nds Tds Tnds BAR
3x/3x 125 65.1 1.9
2x/3x 125 66.9 1.9
3x/2x 125 63.4 2
2x/2x 125 65.1 1.9
*used 45(32.6/16.9) due to discrepancies in listed measurements

Ultegra 6700
ds/nds Tds Tnds BAR
3x/3x 125 61 2.1
2x/3x 125 62.7 2
3x/2x 125 59.4 2.1

Considering the above, the following thoughts develop:
1. There is no hub that is the best for everything and everyone. The trick and the value of the wheel builder is to find the best compromise for the rider/use.
2. BAR ranges from 1.8 to 2.4. Some consider 2.0 a viable compromise between stiffness and stability for the average rider. Heavier, more powerfull riders will do best going above that while keeping the Tnds at check.
3. Tnds ranges from 52kgf to 69kgf. IMO, anything above 65kgf is excellent. Above 60kgf is pretty good. Below 55kgf I would use Spokeprep. Below 50kgf I would not use the hub. Notice I used 125kgf for Tds to help Tnds a bit, however I would not do that for a light weight or box shaped rim.
4. Interestingly enough the DT 240 shows decent numbers; better than hubs I expected to show better. However, i should note that I did find quite a discrepancy on the flange dimensions depending where I looked. Finally I used the numbers from a source I consider reliable. You will do best measuring the hub yourselves as is not clear whether the flange thickness is accounted for from any of the manufacturer's published data.
5. Differences between Xs are very subtle.

I hope it helps somebody to build a better wheel.

cheers

EDIT: The BAR values between 2x/3x and 3x/2x were mistakenly reversed due to a typo. Thanks to orfitinho for bringing it to my attention.

 

[Mackers]

Your BAR makes the DT 240 look good because it has poor bracing angles/flange spacing on both sides.

 

[dcgriz]

Your BAR makes the DT 240 look good because it has poor bracing angles/flange spacing on both sides.

Considering all I've heard about how "noodly" this hub is, I expected worst numbers than a bracing angle ratio of 1.9.

The DS bracing angle (offset of 16.9) is really pretty close to a lot of the 11s hubs. The NDS 32.6 is low relative to others but it appears its done to allow the NDS tension to increase to pretty decent range.

Would I use this hub for my purpose? No, as I favor higher lateral stiffness at the expense of lower tension at the NDS and thankfully there are other choices available to suit me better.

Would that hub be sufficient for a light rider, especially one with low to moderate power output? IMO, absolutely yes. I think it will built to a decent wheel for the right person or use. The 65 kgf on the NDS is a pretty solid number.

Selecting a hub on geometry is a compromise between stiffness and stability. How far you go either way is depends on what you want to do with it.

 

[dcgriz]

The BAR values between 2x/3x and 3x/2x were mistakenly reversed due to a typo. Thanks to orfitinho for bringing it to my attention.
The BAR values of the opening post have been ammended.

 

[jmorgan]

CK R45 S10

nds/ds Tds Tnds BAR
3x/3x 125 68.7 1.82
3x/2x 125 70.8 1.77
2x/3x 125 66.6 1.9

CK looks better or the same as Alchemy . I always thought Alchemy would be better, I guess it's due to the larger flanges on CK.

 

[dcgriz]

CK R45 S10

nds/ds Tds Tnds BAR
3x/3x 125 68.7 1.82
3x/2x 125 70.8 1.77
2x/3x 125 66.6 1.9

CK looks better or the same as Alchemy . I always thought Alchemy would be better, I guess it's due to the larger flanges on CK.

The 2013 CK R45 for S10 uses the same geometry as the 2012 R45 for C11. The numbers you run appear to be for the 2012 R45 S10 which, I understand, is no longer in production.

The Alchemy (3x/3x, 67.4, 1.9) shows better stiffness and at Tnds=67.4 slightly less tension than the 2012 R45.

There is a very small difference due to the height of the flange but its typically eclipsed by the center-flange offset. The reason Alchemy shows better stiffness is because of the offset they have although they keep a shorter left flange thant the R45.

The incremental difference between some of these values is too small to maybe make a rider detectable difference under real life conditions but the numbers are the numbers and the more we understand what they stand for, the better wheels we could build.

 

[svard75]

Hey dcgriz, thanks for the comprehensive table above. Just wondering how would I calculate these values for a build with radial NDS?

 

[dcgriz]

Hey dcgriz, thanks for the comprehensive table above. Just wondering how would I calculate these values for a build with radial NDS?

You follow the same process as with the crosses. I use Rinard's spocalc for the bracing angle. He does not show the angle for radial but you can see the progression from 4x to 1x and either adjust accordingly or calculate it from scratch.

I dont do radial as I see no value other than, maybe, aesthetics so cant help you more on this.

 

[dcgriz]

@svard75

Well......I looked into the spreadsheet and its really simple to modify to include the bracing angles for radial lacing.

Use the following formulas for the REAR wheel radial lacing:

Left. =DEGREES(ASIN($D$32/E24))
Right. =DEGREES(ASIN($D$32/F24))

Let me know if it works for you. The difference is within a 0.1 degree from the 1x angle. E24 and F24 are the spreadsheet cells for the spoke length.

Edit to add: I run a few trials with different hubs for radial NDS and 3x DS and I show the same stiffness as with 2x NDS and 3x DS but with slightly reduced Tnds.

 

[jmorgan]

The 2013 CK R45 for S10 uses the same geometry as the 2012 R45 for C11. The numbers you run appear to be for the 2012 R45 S10 which, I understand, is no longer in production.

The Alchemy (3x/3x, 67.4, 1.9) shows better stiffness and at Tnds=67.4 slightly less tension than the 2012 R45.

There is a very small difference due to the height of the flange but its typically eclipsed by the center-flange offset. The reason Alchemy shows better stiffness is because of the offset they have although they keep a shorter left flange thant the R45.

The incremental difference between some of these values is too small to maybe make a rider detectable difference under real life conditions but the numbers are the numbers and the more we understand what they stand for, the better wheels we could build.

You are correct 2012 CK R45 S10. Do you know how much BAR effects stiffness? For example 3x/3x is 1.82 and 2x/3x (nds/ds) is 1.9. Would that make any noticeable difference?

 

[dcgriz]

You are correct 2012 CK R45 S10. Do you know how much BAR effects stiffness? For example 3x/3x is 1.82 and 2x/3x (nds/ds) is 1.9. Would that make any noticeable difference?

That's a difficult question to answer in absolute terms because it depends on where the stiffness threshold of rubbing pads ( the most common way to detect lack of stiffness short of a power meter) is for each rider and use.
A heavy, strong rider climbing a steep grade acutely tilting his bike left to right will have a higher BAR number as his threshold than a heavy rider riding the flats at moderate output.

To further complicate things, the rim rigidity in conjunction with the spoke system rigidity imposes an additional set of variables that does not allow for an absolute value of BAR to be accurately set for all people at all circumstances.

Roues Artisanales did a series of tests in 2008 on static wheel deflection and found, amongst other things, that increasing the bracing angle is a prerequisite in developing a laterally stiff wheel.
This is the premise of this thread. When I begin selecting components for my builds, I do this analysis to select the hub that potentially gives me the best foundation for a stiff wheel. What is the best foundation as far as BAR goes? For me it is the highest I can achieve keeping Tnds at check. Would I be able to achieve the same wheel stiffness by going a bit less on the BAR and compensate with more or stiffer spokes, deeper rim, etc? I believe so but why take the chance?
It's like building the foundations for a house. Do you build them as strong as just before the house starts to tilt?

I'm sorry I can not give you a direct, absolute term, answer to your question. I believe the answer needs to be empirically developed for each one of us based on our circumstance. However if your past experience has shown you that you belong in the group of riders that could benefit from a stiffer wheel then I suggest you begin with the best geometry hub available and go from there. My desired minimum BAR range is 2.1 - 2.2.

It is my impression that a lot of people begin the wheel building process without such analysis and that's what prompted me to start this thread..

Sorry for the long answer.

 

[Clipped_in]

I hope it helps somebody to build a better wheel.

cheers

Great information! Thanks

 

[jmorgan]

I question the usefulness of BAR. Higher BAR should mean a stiffer wheel (according to you and others), but 2012 CK and Alchemy S10 hubs are ~1.85 BAR and I don't think anyone would say they are not stiff enough. Perhaps the higher tension nds spokes off-set this but then it would suggest Tnds is more important then BAR in creating a stiff wheel. WI T11 builds ~2.3 BAR (3x) but tension being 10+kpf less then CK or Alchemy builds to arguably a wheel that is not as stiff.

Higher BAR = less Tnds, while less BAR = more Tnds.

So really what's the usefulness?

Comparing similar hubs since the measurements are the same except moved over:
2x 588ERD 24 spoke
Tds Tnds BAR
2012 CK R45 S10 125 68.64 1.82
2013 CK R45 S11 125 59.40 2.11

If BAR was more important the 2013 should build a stiffer wheel but I don't see that occurring. 2013 has decent Tnds and a higher BAR, but I think most people would say the 2012 will build a stiffer wheel. (some quick calculations, 2012 should build 6-10% stiffer then 2013)

The only thing I see using BAR for is relative tension difference with 2.0=50% Tnds vs Tds with higher being less then 50% and less being higher Tnds.

 

[dcgriz]

I question the usefulness of BAR. Higher BAR should mean a stiffer wheel (according to you and others), but 2012 CK and Alchemy S10 hubs are ~1.85 BAR and I don't think anyone would say they are not stiff enough. Perhaps the higher tension nds spokes off-set this but then it would suggest Tnds is more important then BAR in creating a stiff wheel. WI T11 builds ~2.3 BAR (3x) but tension being 10+kpf less then CK or Alchemy builds to arguably a wheel that is not as stiff.

Higher BAR = less Tnds, while less BAR = more Tnds.

So really what's the usefulness?

Comparing similar hubs since the measurements are the same except moved over:
2x 588ERD 24 spoke
Tds Tnds BAR
2012 CK R45 S10 125 68.64 1.82
2013 CK R45 S11 125 59.40 2.11

If BAR was more important the 2013 should build a stiffer wheel but I don't see that occurring. 2013 has decent Tnds and a higher BAR, but I think most people would say the 2012 will build a stiffer wheel. (some quick calculations, 2012 should build 6-10% stiffer then 2013)

The only thing I see using BAR for is relative tension difference with 2.0=50% Tnds vs Tds with higher being less then 50% and less being higher Tnds.

BAR/Tnds is nothing more than a awareness tool available to hopefully assist in easily comparing the stiffness vs. stability merits of the available hubs, at least on a tabulation format, as I showed before. I personally find it usefull to possibly help the custom wheel buyer think about what he wants out of the wheel and also help the wheelbuilder easily, and at a glance, sort through different hubs and lacing possibilities.

The concept of the Bracing Angle and Bracing Angle Ratio (BAR) have been around for a long while; their importance in building a good wheel unquestionably accepted. The acronym BAR I came up with is new because I got tired of typing..

Selecting the best hub for the job is deciding where in the stiffness vs. stability (read lateral stability or tension) range you need to be in order to be best served. Some may favor extra stiffness and are willing to do so at the expense of Tnds. Others may be quite opposite.

IMO, tabulating the results in the format I showed before helps in easier identifying the prospects better suited for the job. The hub comparison article from Fairwheel and rruff indicated that the bracing angle ratio of around 2 of being a good compromise between stifness and stability. I think this is a good benchmark to follow. If you are heavier, or heavier and stonger and you dislike flexy wheels then your benchmark number may be 2.2. If you are lighter and capable of only moderate output then 1.8 may better represent you. Eventually and empirically you will end up with what is the best number for you.

The Tnds value tabulated next to the BAR shows the price you need to pay to gain the extra stiffness. My personal threshold, from the wheel building side and for my wheels, is 55kgf. I got to have a very good reason to go below that. Most builders would not want to go below 50. A value in the mid 60s is golden. Your number may be anyplace between 50 and 65.

I have previously discussed the merits of starting the wheel build using the optimized hub geometry as the foundation of where you want the wheel to end up being so I will not repeat it again. Lastly, I would like to leave you with the thought that the latest development with the Shimano 11 speed drives made the Shimano hubs as compromised as the Campy and that's why tools like the BAR/Tnds are becoming even more important helping to decipher the best performing hub for the application.

 

[jmorgan]

Selecting the best hub for the job is deciding where in the stiffness vs. stability (read lateral stability or tension) range you need to be in order to be best served. Some may favor extra stiffness and are willing to do so at the expense of Tnds. Others may be quite opposite.

My post above questions just this.

You say BAR is important and higher is better, that would mean WI T11 should build a stiffer wheel then Alchemy ORC-UL.

WI T11 BAR 2.3
ORC-UL S10 BAR 1.88
ORC-UL S11 BAR 2.12

Your logic implies WI will build the stiffest lateral wheel possible (out of the ones we have kind of talked about). We all know that is not true.

Your logic would suggest getting WI T11 and use spoke prep to keep the spokes from backing out. That will result in a stiffer wheel then the ORC-UL based on BAR alone.

Im saying nds spoke tension is a better predictor of a stiff wheel then BAR. CK and Alchemy with there small BAR will build a stiffer wheel then WI and their high BAR.

I think you are forgetting what BAR is equal to. (2012 CK)
BAR = nds angle/ ds angle (7/3.8=1.82)

or for a faster comparison:
center to left flange/ center to right flange (34.6/18.9=1.83)

and

Tds/BAR=Tnds
125kpf/1.82= 68.7 Tnds


You are saying a smaller BAR produces a wheel that is less stiff. BAR is directly related to the resulting Tnds. A lower BAR produces higher Tnds, while a higher BAR produces a lower Tnds.

 

[dcgriz]

My post above questions just this.

You say BAR is important and higher is better, that would mean WI T11 should build a stiffer wheel then Alchemy ORC-UL.

WI T11 BAR 2.3
ORC-UL S10 BAR 1.88
ORC-UL S11 BAR 2.12

Your logic implies WI will build the stiffest lateral wheel possible (out of the ones we have kind of talked about). We all know that is not true.
.

You are missing the point. BAR is a ratio inclusive of the effects of tension and not an absolute value. The NDS bracing angle is an absolute value. A hub with the largest possible NDS bracing angle would build the stiffest wheel but this wheel would collapse on itself before you reached the end of the block.

 

[jmorgan]

You are missing the point. BAR is a ratio inclusive of the effects of tension and not an absolute value. The NDS bracing angle is an absolute value. A hub with the largest possible NDS bracing angle would build the stiffest wheel but this wheel would collapse on itself before you reached the end of the block.

So WI T11 will build a stiffer wheel then the ORC-UL?

 

[dcgriz]

So WI T11 will build a stiffer wheel then the ORC-UL?

ok....lets try again

Wheel stiffness is a factor of lateral stiffness, torsional stiffness and radial stiffness. In other words stiffness from hub geometry + stiffness from rim + stiffness from spokes. You got to have all three working together to build a stiff wheel. For our case we are only talking about the efect of hub geometry to lateral stifness and assume all other factors are equal.

The ORC-S11 shows comparable results to the T-11. Its got almost the same left offset angle so stiffness will be comparable but it shows a modestly better tension balance which means it may be able to sustain the wheel integrity (durability) longer when exposed to the same conditions as the T-11.

You should not look into this in absolute terms especially when considering only one of the variables at play.


EDIT TO ADD: I forgot to add "Over and out". I'm tired of typing. :ihih:

 

[jmorgan]

It's one variable when everything else is left the same, same rim, same spokes (very slight difference in length, that's it). This isn't rocket science. It's angles and tension.

Sorry but you are just dancing around the issue and talking in super general terms and not backing it up with science. Your argument is the they have a "similar left offset" so they would be similar. But let's not forget, the right side which has a measurable difference in offset and tension itself plays a role in wheel stiffness.

Your argument is BAR dictates wheel stiffness and a higher BAR equals a stiffer wheel. Funny how the hubs regarded as being the stiffest have the lowest BAR. Show me some science that contradicts that.

 

[dcgriz]

It's one variable when everything else is left the same, same rim, same spokes (very slight difference in length, that's it). This isn't rocket science. It's angles and tension.

Sorry but you are just dancing around the issue and talking in super general terms and not backing it up with science. Your argument is the they have a "similar left offset" so they would be similar. But let's not forget, the right side which has a measurable difference in offset and tension itself plays a role in wheel stiffness.

Your argument is BAR dictates wheel stiffness and a higher BAR equals a stiffer wheel. Funny how the hubs regarded as being the stiffest have the lowest BAR. Show me some science that contradicts that.

Go back and read the thread from the beginning; you are taking my statements out of context. What I said was, when comparing hubs, pick the one with the higher BAR keeping the Tnds at CHECK.

This means if you have two hubs that show the same Tnds @ some BAR value, pick the one with the higher BAR value. If you need an example , use the 2x/3x R45 and ORC s11. If the Tnds is different then you got to use your judgment because you take from stiffness to increase the tension and thus the wheel stability.

You are saying "But let's not forget, the right side which has a measurable difference in offset and tension itself plays a role in wheel stiffness."
Im not sure what you are trying to say here but if you are trying to make a point comparing s10 to s11/c11 that's a lame attempt for an argument. The typical s11/c11 has the right side maxed out or very close to it (16-17mm) and the left is where the play is.